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Assertion and Reasoning:

a) Both assertion and reason are true and reason is the correct explanation of the assertion.
b) Both assertion and reason are true, but reason is not the correct explanation of the assertion.
c) Assertion is true, but reason is false.
d) Assertion is false, but reason is true.

6. Assertion: 0.189 is a terminating decimal.
Reason: A decimal in which a digit or set of digits is repeated periodically is called a repeating or recurring decimal.

7. Assertion: The zeroes of the polynomial [tex]f(x) = x^2 - 5x + 6[/tex] are 3 and 2.
Reason: A linear polynomial has exactly one zero.

Directions: In each of the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Mark the correct answer.

Sagot :

Let's analyze each assertion and its corresponding reason.

### Question 6:
- Assertion: 0.189 is a terminating decimal.
- Reason: A decimal in which a digit or set of digits is repeated periodically is called a repeating or recurring decimal.

Analysis:
- The assertion states that 0.189 is a terminating decimal. A terminating decimal is a decimal that ends after a finite number of digits.
- The reason provided describes a repeating or recurring decimal, which is a decimal where a digit or group of digits repeat infinitely. Examples include 0.333... and 0.142857142857...

Conclusion for Question 6:
- The assertion is true because 0.189 is indeed a terminating decimal.
- The reason is also true; it correctly defines a repeating or recurring decimal.
- However, the reason does not provide an explanation for the assertion.

Correct Answer for Question 6: (b) Both assertion and reason are true but reason is not the correct explanation of assertion.

### Question 7:
- Assertion: The zeroes of the polynomial [tex]\( f(x) = x^2 - 5x + 6 \)[/tex] are 3 and 2.
- Reason: A linear polynomial has exactly one zero.

Analysis:
- The assertion states that the zeroes of the quadratic polynomial [tex]\( x^2 - 5x + 6 \)[/tex] are 3 and 2. We can verify this by factoring the polynomial: [tex]\( x^2 - 5x + 6 = (x - 3)(x - 2) \)[/tex]. Setting each factor to zero, we get the solutions [tex]\( x = 3 \)[/tex] and [tex]\( x = 2 \)[/tex].
- The reason states that a linear polynomial has exactly one zero, which is indeed true. A linear polynomial of the form [tex]\( ax + b = 0 \)[/tex] will have exactly one solution, [tex]\( x = -\frac{b}{a} \)[/tex].

Conclusion for Question 7:
- The assertion is true as the solutions to the polynomial are indeed 3 and 2.
- The reason is true; a linear polynomial does have exactly one zero.
- However, the reason is unrelated to the assertion, making the reason false in the context of explaining the assertion.

Correct Answer for Question 7: (c) Assertion is true, but reason is false.

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### Summary:
Assertions and reasons evaluated in each question match the conclusions derived above.

- For question 6, the correct answer is (b).
- For question 7, the correct answer is (c).